How to make torch cutting logo out of a plane (steel) and falling pieces.?
Starting with a plane, you can use the knife tool K to cut a logo into it.



Then in face select mode select the faces you want to come out. Use P->Selection to break the selected faces into a new object that are located at the same position, so both objects will blend in as one. Note that a subsurf modifier will pull the edges apart and make the seam visible.

Now you animate the location of the piece you want to fall. Go to the frame you want it in place, say 20, and press I->LocRot to add a keyframe for the location and rotation. Move ahead a few frames and move the logo and add another keyframe. Repeat a few times to have it move and rotate as you want.



For the effects you can combine that animation with dynamic paint and particles.